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Summary:
Blind image deblurring is a challenging ill-posed problem. It would have an infinite number of solutions even in cases when an observed image contains no noise. In reality, however, observed images almost always contain noise. The presence of noise would make the image deblurring problem even more challenging because the noise can cause numerical instability in many existing image deblurring procedures. In this article, a novel blind image deblurring approach is proposed, which can remove both pointwise noise and spatial blur efficiently without imposing restrictive assumptions on either the point spread function (psf) or the true image. It even allows the psf to be location dependent. In the proposed approach, a local pixel clustering procedure is used to handle the challenging task of restoring complicated edge structures that are tapered by blur, and a nonparametric regression procedure is used for removing noise at the same time. Numerical examples show that our proposed method can effectively handle a wide variety of blur and it works well in applications. Supplementary materials for this article are available online.

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